If 30 persons take 10 days to complete a work by working 8 hours a day, then 40 persons should work how many hours a day to complete the work in 6 days?

1. A

   8 hours

2. B

   12 hours

3. C

   10 hours

4. D

   6 hours

Appeared in: UPPSC 2023

Explanation

• The problem is based on the principle that the total amount of work (measured in person-hours) is constant.
• The formula M₁ × D₁ × H₁ = M₂ × D₂ × H₂ is used, where M is men, D is days, and H is hours.
• First, calculate the total work: 30 persons × 10 days × 8 hours/day = 2400 person-hours.
• Then, solve for the unknown hours (H₂) in the second scenario: 2400 = 40 persons × 6 days × H₂.
• Solving the equation gives H₂ = 2400 / (40 × 6) = 2400 / 240 = 10 hours.

Why Other Options Were Wrong

• Option A: Working 8 hours a day would only produce 1920 person-hours (40 × 6 × 8), which is insufficient to complete the 2400 person-hour job.
• Option B: Working 12 hours a day would produce 2880 person-hours (40 × 6 × 12), which is more than the required 2400 person-hours.
• Option D: Working 6 hours a day would only produce 1440 person-hours (40 × 6 × 6), which is far below the required 2400 person-hours.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Time and Work Problems as background academic context rather than a clinical decision trigger.
• While not a clinical question, this type of logical reasoning is crucial for nurses in tasks like resource management, staffing assignments, and calculating medication schedules.
• For example, if it takes 2 nurses 4 hours to admit 8 patients, a nurse manager can use similar logic to estimate how many nurses are needed to admit 12 patients in the same timeframe.
• This skill helps in efficient planning and ensures that tasks are completed on time, which is critical for patient care and safety.

How to Approach the Question

• First, identify that this is a 'Time and Work' problem involving multiple variables (persons, days, hours).
• Recognize that the total amount of work done is the same in both scenarios.
• Recall or derive the formula that equates the work in both scenarios: M₁ × D₁ × H₁ = M₂ × D₂ × H₂.
• Carefully substitute the given values from the question into the formula. Let the unknown value be a variable (e.g., H₂).
• Calculate the product on the side of the equation with all known values (30 × 10 × 8 = 2400).
• Solve the resulting algebraic equation for the unknown variable (H₂ = 2400 / 240).

Concept Tested & Keywords

• Concept Tested: Time and Work Problems
• Stem keywords: persons, days, complete a work, hours a day
• Lead-in keywords: how many
• Negative lead-in flag: false

Question ID

QavxRfYqVIN2sjPz6QB7IJ

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